According to [1]}, in order to augment the model with some
kind of target interaction, one needs to jointly estimate the state of all
targets. A joint particle filter in which the state is \({X_t = \lbrace X_{it}|i \in 1..n\rbrace }\)  can be used to track n targets. However, this increased complexity in state
space makes the filter exponentially complex with the number of targets.
To go around such complexity, fewer particles could be used but this would result in undersampling of the state space, making the filter perform poorly. For this reason, a MCMC sampling step is used in the referenced approach
so that the low complexity of independent particle filters, augmented with an interaction model, could be used.
